English

On Koebe radius and coefficients estimate for univalent harmonic mappings

Complex Variables 2025-05-06 v2

Abstract

The problem on estimate of the Koebe radius for univalent harmonic mappings of the unit disk D={zC:z<1}\mathbb D=\{z\in\mathbb C : |z|<1\} is considered. For a subclass of harmonic mappings with the standard normalization and a certain growth estimate for analytic dilatation, we provide new estimate for the Koebe radius. New estimate for Taylor coefficients of the holomorphic part of a function from the subclass under consideration is obtained as a corollary.

Keywords

Cite

@article{arxiv.2403.05526,
  title  = {On Koebe radius and coefficients estimate for univalent harmonic mappings},
  author = {Mikhail Borovikov},
  journal= {arXiv preprint arXiv:2403.05526},
  year   = {2025}
}
R2 v1 2026-06-28T15:13:55.668Z